SET007 Axioms: SET007+560.ax
%------------------------------------------------------------------------------
% File : SET007+560 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Lawson Topology in Continuous Lattices
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : waybel21 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 73 ( 0 unt; 0 def)
% Number of atoms : 1107 ( 39 equ)
% Maximal formula atoms : 27 ( 15 avg)
% Number of connectives : 1171 ( 137 ~; 1 |; 765 &)
% ( 15 <=>; 253 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 65 ( 64 usr; 0 prp; 1-4 aty)
% Number of functors : 28 ( 28 usr; 0 con; 1-5 aty)
% Number of variables : 247 ( 235 !; 12 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_waybel21,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B) ) ) ) ) ).
fof(cc2_waybel21,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel21(C,A,B)
=> ( v1_relat_1(C)
& v19_waybel_0(C,A,B) ) ) ) ).
fof(rc1_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& v7_yellow_0(B,A)
& v3_waybel_0(B,A)
& v4_waybel_0(B,A)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ).
fof(fc1_waybel21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_yellow_9(A,k1_struct_0(A,B)))
& v2_orders_2(k3_yellow_9(A,k1_struct_0(A,B)))
& v3_orders_2(k3_yellow_9(A,k1_struct_0(A,B)))
& v6_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
& v7_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)))
& v8_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
& v9_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
& v10_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A)
& v11_waybel_0(k3_yellow_9(A,k1_struct_0(A,B)),A) ) ) ).
fof(rc2_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v6_waybel_0(B,A)
& v7_waybel_0(B)
& v8_waybel_0(B,A)
& v9_waybel_0(B,A)
& v10_waybel_0(B,A)
& v11_waybel_0(B,A) ) ) ).
fof(fc2_waybel21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k3_yellow_9(A,B))
& v6_waybel_0(k3_yellow_9(A,B),A)
& v9_waybel_0(k3_yellow_9(A,B),A) ) ) ).
fof(fc3_waybel21,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ~ v3_struct_0(D)
& v9_waybel_0(D,A)
& l1_waybel_0(D,A) )
=> ( ~ v3_struct_0(k7_waybel_9(A,B,C,D))
& v6_waybel_0(k7_waybel_9(A,B,C,D),B)
& v9_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ).
fof(d1_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ( v2_yellow_0(A)
=> v2_yellow_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( m1_waybel21(C,A,B)
<=> ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) ) ) ) ) ) ) ).
fof(t1_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel21(C,A,B)
=> k3_yellow_6(u1_struct_0(A),B,C,k4_yellow_0(A)) = k4_yellow_0(B) ) ) ) ).
fof(t2_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v19_waybel_0(C,A,B)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) ) ) ) ) ) ).
fof(t3_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( k3_yellow_6(u1_struct_0(A),B,C,k4_yellow_0(A)) = k4_yellow_0(B)
=> m1_waybel21(C,A,B) ) ) ) ) ).
fof(t4_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v19_waybel_0(C,A,B)
& ! [D] :
( ( ~ v1_xboole_0(D)
& v2_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) ) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) ) ) ) ) ) ).
fof(t5_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v17_waybel_0(C,A,B)
=> m1_waybel21(C,A,B) ) ) ) ) ).
fof(t6_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
& g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( E = F
=> ( ( v17_waybel_0(E,A,B)
=> v17_waybel_0(F,C,D) )
& ( v22_waybel_0(E,A,B)
=> v22_waybel_0(F,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
& g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( E = F
=> ( ( v18_waybel_0(E,A,B)
=> v18_waybel_0(F,C,D) )
& ( v21_waybel_0(E,A,B)
=> v21_waybel_0(F,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> v17_waybel_0(k1_yellow_9(A,B),B,A) ) ) ).
fof(t9_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v8_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> v18_waybel_0(k1_yellow_9(A,B),B,A) ) ) ).
fof(t10_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> v22_waybel_0(k1_yellow_9(A,B),B,A) ) ) ).
fof(t11_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v3_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> v21_waybel_0(k1_yellow_9(A,B),B,A) ) ) ).
fof(t12_waybel21,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( l1_orders_2(C)
=> ! [D] :
( m1_yellow_0(D,A)
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C)) )
=> ( m1_yellow_0(C,B)
& ( v4_yellow_0(D,A)
=> ( v4_yellow_0(C,B)
& m1_yellow_0(C,B) ) ) ) ) ) ) ) ) ).
fof(t13_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v4_yellow_0(A,A)
& v7_yellow_0(A,A)
& v8_yellow_0(A,A)
& m1_yellow_0(A,A) ) ) ).
fof(t14_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v5_yellow_0(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ).
fof(t15_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v6_yellow_0(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ).
fof(t16_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( ( r2_hidden(k4_yellow_0(A),u1_struct_0(B))
& v3_waybel_0(B,A) )
=> v7_yellow_0(B,A) ) ) ) ).
fof(t17_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v6_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( ( r2_hidden(k3_yellow_0(A),u1_struct_0(B))
& v4_waybel_0(B,A) )
=> v8_yellow_0(B,A) ) ) ) ).
fof(t18_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v7_yellow_0(B,A)
=> v3_lattice3(B) ) ) ) ).
fof(t19_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v8_yellow_0(B,A)
=> v3_lattice3(B) ) ) ) ).
fof(t20_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,B)
& m1_yellow_0(D,B) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& u1_struct_0(C) = u1_struct_0(D)
& v7_yellow_0(C,A) )
=> v7_yellow_0(D,B) ) ) ) ) ) ).
fof(t21_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,B)
& m1_yellow_0(D,B) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& u1_struct_0(C) = u1_struct_0(D)
& v8_yellow_0(C,A) )
=> v8_yellow_0(D,B) ) ) ) ) ) ).
fof(t22_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,B)
& m1_yellow_0(D,B) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& u1_struct_0(C) = u1_struct_0(D)
& v4_waybel_0(C,A) )
=> v4_waybel_0(D,B) ) ) ) ) ) ).
fof(t23_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,B)
& m1_yellow_0(D,B) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& u1_struct_0(C) = u1_struct_0(D)
& v3_waybel_0(C,A) )
=> v3_waybel_0(D,B) ) ) ) ) ) ).
fof(t24_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(D,A,B)
=> r1_tarski(k4_pre_topc(A,B,D,k11_yellow_6(A,C)),k11_yellow_6(B,k7_waybel_9(A,B,D,C))) ) ) ) ) ) ).
fof(d2_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( v9_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_orders_2(B,C,D)
=> r1_orders_2(A,k3_waybel_0(A,B,D),k3_waybel_0(A,B,C)) ) ) ) ) ) ) ).
fof(t27_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r1_tarski(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)),C)
=> r1_waybel_0(A,B,C) ) ) ) ).
fof(t28_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_waybel11(A,k3_yellow_9(A,B)) = k2_yellow_0(A,B) ) ) ).
fof(t29_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v25_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> k1_waybel11(B,k7_waybel_9(A,B,D,k3_yellow_9(A,C))) = k2_yellow_0(B,k4_pre_topc(A,B,D,C)) ) ) ) ) ).
fof(t30_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v2_waybel_0(E,B)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
=> ( E = k4_pre_topc(A,B,D,C)
=> m2_yellow_6(k7_waybel_9(A,B,D,k3_yellow_9(A,C)),B,k3_yellow_9(B,E)) ) ) ) ) ) ) ).
fof(t31_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v2_waybel_0(E,B)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
=> ( E = k4_pre_topc(A,B,D,C)
=> r1_tarski(k11_yellow_6(B,k3_yellow_9(B,E)),k11_yellow_6(B,k7_waybel_9(A,B,D,k3_yellow_9(A,C)))) ) ) ) ) ) ) ).
fof(t32_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( u1_waybel_0(A,k4_waybel17(A,B)) = k6_relat_1(B)
& u1_struct_0(k4_waybel17(A,B)) = B
& v4_yellow_0(k4_waybel17(A,B),A)
& m1_yellow_0(k4_waybel17(A,B),A) ) ) ) ).
fof(t33_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_waybel11(B,k7_waybel_9(A,B,C,k4_waybel17(A,D))) = k1_yellow_0(B,k4_pre_topc(A,B,C,D)) ) ) ) ) ).
fof(t34_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_waybel17(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k4_waybel17(A,B)))
=> ( r3_orders_2(k4_waybel17(A,B),C,D)
<=> r3_orders_2(A,k3_waybel_0(A,k4_waybel17(A,B),C),k3_waybel_0(A,k4_waybel17(A,B),D)) ) ) ) ) ) ).
fof(t35_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_hidden(k1_yellow_0(A,B),k11_yellow_6(A,k4_waybel17(A,B))) ) ) ).
fof(d3_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> ( m2_yellow_6(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ( m2_waybel21(D,A,B,C)
<=> ( u1_waybel_0(A,C) = k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,u1_waybel_0(A,B))
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(C))
& ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( r1_orders_2(C,F,G)
=> r1_orders_2(B,E,k3_yellow_6(u1_struct_0(C),B,D,G)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m2_yellow_6(C,A,B) )
=> ! [D] :
( m2_waybel21(D,A,B,C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k3_waybel_0(A,C,E) = k3_waybel_0(A,B,k3_yellow_6(u1_struct_0(C),B,D,E)) ) ) ) ) ) ).
fof(t37_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m2_yellow_6(C,A,B)
=> r3_orders_2(A,k1_waybel11(A,B),k1_waybel11(A,C)) ) ) ) ).
fof(t38_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m2_yellow_6(C,A,B)
=> ! [D] :
( m2_waybel21(D,A,B,C)
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ~ ( r1_orders_2(B,k3_yellow_6(u1_struct_0(C),B,D,F),E)
& ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ~ ( r1_orders_2(C,F,G)
& r1_orders_2(A,k3_waybel_0(A,C,G),k3_waybel_0(A,B,E)) ) ) ) ) )
=> k1_waybel11(A,B) = k1_waybel11(A,C) ) ) ) ) ) ).
fof(t39_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_yellow_6(C,A,B)
& m1_yellow_6(C,A,B) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& r1_orders_2(B,D,E)
& r2_hidden(E,u1_struct_0(C)) ) )
=> ( m2_yellow_6(C,A,B)
& m2_waybel21(k1_yellow_9(B,C),A,B,C) ) ) ) ) ) ).
fof(t40_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( m2_yellow_6(k6_waybel_9(A,B,C),A,B)
& m2_waybel21(k1_yellow_9(B,k6_waybel_9(A,B,C)),A,B,k6_waybel_9(A,B,C)) ) ) ) ) ).
fof(t41_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k1_waybel11(A,k6_waybel_9(A,B,C)) = k1_waybel11(A,B) ) ) ) ).
fof(t42_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
~ ( r1_waybel_0(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ~ ( r2_hidden(k3_waybel_0(A,B,D),C)
& r1_tarski(k8_yellow_2(u1_struct_0(k6_waybel_9(A,B,D)),A,u1_waybel_0(A,k6_waybel_9(A,B,D))),C) ) ) ) ) ) ).
fof(t43_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v11_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> ( ~ v1_xboole_0(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)))
& v2_waybel_0(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)),A)
& m1_subset_1(k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t44_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v11_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> k11_yellow_6(A,B) = k1_struct_0(A,k2_waybel_9(A,B)) ) ) ).
fof(t45_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel19(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(C,A,B)
<=> ( v22_waybel_0(C,A,B)
& ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,B,C,D) ) ) ) ) ) ) ).
fof(t46_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel19(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_waybel21(C,A,B)
=> ( v5_pre_topc(C,A,B)
<=> ( v17_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ) ) ) ).
fof(d4_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_waybel21(C,A,B)
<=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> k3_yellow_6(u1_struct_0(A),B,C,k1_waybel11(A,D)) = k1_waybel11(B,k7_waybel_9(A,B,C,D)) ) ) ) ) ) ).
fof(t47_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v2_waybel19(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_waybel21(C,A,B)
=> ( v5_pre_topc(C,A,B)
<=> v1_waybel21(C,A,B) ) ) ) ) ).
fof(t48_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( r2_hidden(k4_yellow_0(A),u1_struct_0(B))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( C = u1_struct_0(B)
& v4_pre_topc(C,A) ) )
| v7_yellow_0(B,A) ) ) ) ) ).
fof(t49_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& C = u1_struct_0(B)
& v4_pre_topc(C,A) )
=> v4_waybel_0(B,A) ) ) ) ).
fof(t50_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& C = u1_struct_0(B)
& v4_pre_topc(C,A) ) ) ) ).
fof(t51_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r1_waybel_0(A,C,u1_struct_0(B))
=> r2_hidden(k1_waybel11(A,C),u1_struct_0(B)) ) ) ) ) ).
fof(t52_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( ( r2_hidden(k4_yellow_0(A),u1_struct_0(B))
& ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r1_tarski(k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C)),u1_struct_0(B))
=> r2_hidden(k1_waybel11(A,C),u1_struct_0(B)) ) ) )
=> v7_yellow_0(B,A) ) ) ) ).
fof(t53_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( r1_tarski(k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C)),u1_struct_0(B))
=> r2_hidden(k1_waybel11(A,C),u1_struct_0(B)) ) )
=> v4_waybel_0(B,A) ) ) ) ).
fof(t54_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v3_waybel_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel19(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( C = u1_struct_0(B)
& r2_hidden(k4_yellow_0(A),C) )
=> ( v4_pre_topc(C,A)
<=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ( r1_waybel_0(A,D,C)
=> r2_hidden(k1_waybel11(A,D),C) ) ) ) ) ) ) ) ).
fof(dt_m1_waybel21,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel21(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ).
fof(existence_m1_waybel21,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ? [C] : m1_waybel21(C,A,B) ) ).
fof(dt_m2_waybel21,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( m2_waybel21(D,A,B,C)
=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) ) ) ) ).
fof(existence_m2_waybel21,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& ~ v3_struct_0(C)
& l1_waybel_0(C,A) )
=> ? [D] : m2_waybel21(D,A,B,C) ) ).
fof(t25_waybel21,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v1_xboole_0(a_2_0_waybel21(A,B))
& v1_waybel_0(a_2_0_waybel21(A,B),A)
& m1_subset_1(a_2_0_waybel21(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t26_waybel21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v8_waybel_0(B,A)
& l1_waybel_0(B,A) )
=> ( ~ v1_xboole_0(a_2_1_waybel21(A,B))
& v1_waybel_0(a_2_1_waybel21(A,B),A)
& m1_subset_1(a_2_1_waybel21(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(fraenkel_a_2_0_waybel21,axiom,
! [A,B,C] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_0_waybel21(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k2_yellow_0(B,a_3_0_waybel21(B,C,D)) ) ) ) ).
fof(fraenkel_a_3_0_waybel21,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_waybel21(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
fof(fraenkel_a_2_1_waybel21,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v8_waybel_0(C,B)
& l1_waybel_0(C,B) )
=> ( r2_hidden(A,a_2_1_waybel21(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(C))
& A = k2_yellow_0(B,a_3_1_waybel21(B,C,D)) ) ) ) ).
fof(fraenkel_a_3_1_waybel21,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v8_waybel_0(C,B)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_1_waybel21(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
%------------------------------------------------------------------------------